scholarly journals Fredholm determinant for higher dimensional piecewise linear transformations

1999 ◽  
Vol 25 (2) ◽  
pp. 317-342 ◽  
Author(s):  
Makoto MORI
Keyword(s):  
Fredholm Determinant ◽  
Piecewise Linear ◽  
Linear Transformations ◽  
Higher Dimensional

scholarly journals Interconversion of Plasma Free Thyroxine Values from Assay Platforms with Different Reference Intervals Using Linear Transformation Methods

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 45
Author(s):  
Fanwen Meng ◽  
Jacqueline Jonklaas ◽  
Melvin Khee-Shing Leow
Keyword(s):  
Linear Transformation ◽  
Piecewise Linear ◽  
Equilibrium Dialysis ◽  
Accurate Method ◽  
Reference Intervals ◽  
Thyroid Stimulating Hormone ◽  
Free Thyroxine ◽  
Thyroid Function Tests ◽  
Linear Transformations ◽  
Transformation Methods

Clinicians often encounter thyroid function tests (TFT) comprising serum/plasma free thyroxine (FT4) and thyroid stimulating hormone (TSH) measured using different assay platforms during the course of follow-up evaluations which complicates reliable comparison and interpretation of TFT changes. Although interconversion between concentration units is straightforward, the validity of interconversion of FT4/TSH values from one assay platform to another with different reference intervals remains questionable. This study aims to establish an accurate and reliable methodology of interconverting FT4 by any laboratory to an equivalent FT4 value scaled to a reference range of interest via linear transformation methods. As a proof-of-concept, FT4 was simultaneously assayed by direct analog immunoassay, tandem mass spectrometry and equilibrium dialysis. Both linear and piecewise linear transformations proved relatively accurate for FT4 inter-scale conversion. Linear transformation performs better when FT4 are converted from a more accurate to a less accurate assay platform. The converse is true, whereby piecewise linear transformation is superior to linear transformation when converting values from a less accurate method to a more robust assay platform. Such transformations can potentially apply to other biochemical analytes scale conversions, including TSH. This aids interpretation of TFT trends while monitoring the treatment of patients with thyroid disorders.

Totally knotted knots are prime

1982 ◽  
Vol 91 (3) ◽  
pp. 467-472
Author(s):  
J. C. Gomez-Larran¯aga
Keyword(s):  
Finite Number ◽  
Knot Theory ◽  
Piecewise Linear ◽  
Connected Sum ◽  
Higher Dimensional ◽  
The Family ◽  
Linear Category

Throughout, the word knot means a subspace of the 3-sphere S3 homeomorphic with the 1-sphere S1. Any knot can be expressed as a connected sum of a finite number of prime knots in a unique way (13), we consider the trivial knot a non-prime knot. (For higher dimensional knots, factorization and uniqueness have been studied in (1).) However given a knot it is difficult to determine if it is prime or not. We prove that totally knotted knots, see definition in §2, are prime in theorem 1, give a class of examples in theorem 2 and investigate how the last result can be applied to the conjecture that the family Y of unknotting number one knots are prime. (See problem 2 in (5).) At the end, prime tangles as defined by W. B. R. Lickerish are used to prove that in a certain family of knots, related somewhat to Y, there is just one non-prime knot: the square knot. The paper should be interpreted as being in the piecewise linear category. Standard definitions of 3-manifolds and knot theory may be found in (6) and (11) respectively.

A free group of piecewise linear transformations

2011 ◽  
Vol 125 (2) ◽  
pp. 141-146
Author(s):  
Grzegorz Tomkowicz
Keyword(s):  
Free Group ◽  
Piecewise Linear ◽  
Linear Transformations

Induction of Similarity Measures and Medical Diagnosis Support Rules through Separable, Linear Data Transformations

2006 ◽  
Vol 45 (02) ◽  
pp. 200-203 ◽  
Author(s):  
L. Bobrowski
Keyword(s):  
Medical Diagnosis ◽  
Euclidean Distance ◽  
Piecewise Linear ◽  
Similarity Measures ◽  
Case Based Reasoning ◽  
Data Sets ◽  
Linear Transformations ◽  
Data Transformations ◽  
Criterion Functions ◽  
Learning Data

Summary Objectives: To improve the medical diagnosis support rules based on comparisons of diagnosed patients with similar cases (precedents) archived in a clinical database. The case-based reasoning (CBR) or the nearest neighbors (K-NN) classifications, which operate on referencing (learning) data sets, belong to this scheme. Methods: Inducing similarity measure through special linear transformations of the referencing sets aimed at the best separation of these sets. Designing separable transformations can be based on dipolar models and minimization of the convex and piecewise linear (CPL) criterion functions in accordance with the basis exchange algorithm. Results: Separable linear transformations allow for some data sets to decrease the error rate of the K-NNclassification rule based on the Euclidean distance. Such results can be seen on the example of data sets taken from the Heparsystem of diagnosis support. Conclusions: Medical diagnosis support based on the CBRor the K-NNrules can be improved through separable transformations of the referencing sets.

Multiple Harmonic Balance Method for Aperiodic Vibration of a Piecewise-Linear System

1998 ◽  
Vol 120 (1) ◽  
pp. 181-187 ◽  
Author(s):  
Y. B. Kim
Keyword(s):  
Linear System ◽  
Harmonic Balance ◽  
Piecewise Linear ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Balance Method ◽  
Piecewise Linear System ◽  
Higher Dimensional ◽  
Computational Procedures ◽  
The Stability

A multiple harmonic balance method is presented in this paper for obtaining the aperiodic steady-state solution of a piecewise-linear system. As the method utilizes general and systematic computational procedures, it can be applied to analyze the multi-tone or combination-tone responses for the higher dimensional nonlinear systems such as rotors. Moreover, it is capable of informing the stability of the obtained solution using Floquet theory. To demonstrate the systematic approach of the new method, the almost periodic forced vibration of an articulated loading platform (ALP) with a piecewise-linear stiffness is computed as an example.

DYNAMICAL SYSTEMS FROM QUANTUM INTEGRABILITY

1993 ◽  
Vol 07 (20n21) ◽  
pp. 3567-3596 ◽  
Author(s):  
M.P. Bellon ◽  
J-M. Maillard ◽  
C-M. Viallet
Keyword(s):  
Dynamical Systems ◽  
Projective Spaces ◽  
Linear Transformations ◽  
Quantum Integrability ◽  
Higher Dimensional ◽  
Algebraic Invariants ◽  
Non Linear ◽  
Birational Mappings

We describe a class of non-linear transformations acting on many variables. These transformations have their origin in the theory of quantum integrability: they appear in the description of the symmetries of the Yang-Baxter equations and their higher dimensional generalizations. They are generated by involutions and act as birational mappings on various projective spaces. We present numerous figures, showing successive iterations of these mappings. The existence of algebraic invariants explains the aspect of these figures. We also study deformations of our transformations.

scholarly journals Polynomial approximation on spheres - generalizing de la Vallée-Poussin

2011 ◽  
Vol 11 (4) ◽  
pp. 540-552 ◽  
Author(s):  
Ian H. Sloan
Keyword(s):  
Trigonometric Polynomial ◽  
Polynomial Approximation ◽  
Piecewise Linear ◽  
Continuous Functions ◽  
Fast Convergence ◽  
Piecewise Polynomial ◽  
Smooth Functions ◽  
Higher Dimensional ◽  
Trigonometric Polynomial Approximation ◽  
De La Vallée Poussin

AbstractFor trigonometric polynomial approximation on a circle, the century-old de la Vallée-Poussin construction has attractive features: it exhibits uniform convergence for all continuous functions as the degree of the trigonometric polynomial goes to infinity, yet it also has arbitrarily fast convergence for sufficiently smooth functions. This paper presents an explicit generalization of the de la Vallée-Poussin construction to higher dimensional spheres S^d ≤ R^{d+1}. The generalization replaces the C^∞ filter introduced by Rustamov by a piecewise polynomial of minimal degree. For the case of the circle the filter is piecewise linear, and recovers the de la Vallée-Poussin construction, while for the general sphere S^d the filter is a piecewise polynomial of degree d and smoothness C^{d−1}. In all cases the approximation converges uniformly for all continuous functions, and has arbitrarily fast convergence for smooth functions.

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